Predictive Model for Los Angeles Dodgers Promotion and Attendance
Jimmyxu
October 18, 2018
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## Predictive Model for Los Angeles Dodgers Promotion and Attendance (R)
## by Dr. Jimmy (Zhenning) Xu,
## follow me on Twitter https://twitter.com/MKTJimmyxu
################################################################################Introduction
It is tough to make good predictions. The numerous factors or variables, independent and dependent, involved in many sporting events contribute to the unpredictability. However, using carefully-selected variables, it is still possible to make marketing promotions more accountable.
The goal of this case study is to analyze if bobblehead promotions increase attendance at Dodgers home games. Using the fitted predictive model we can predict the attendance for the game in the forthcomming season and we can predict the attendance with or without bobblehead promotion.
The motivation of this case study is to design a predictive model, and report any interesting findings to support critical business decision making.
Pre-Processing
Load the required libraries and the data
rm(list=ls())# clear memory
setwd("C:/Users/xzhenning/Documents/R/fall 2018/Markdown")
library(car) # Package with Special functions for linear regression## Loading required package: carDatalibrary(lattice) # Graphics Package
library(ggplot2) # Graphical Package
#Create a dataframe with Dodgers Data
DodgersData <- read.csv("DodgersData.csv")Data cleanup and exploratory analysis
Evaluate the Structure and Re-Level the factor variables for “Day Of Week”" and “Month”" in the right order
# Check the structure for Dorder Data
str(DodgersData)## 'data.frame': 81 obs. of 12 variables:
## $ month : Factor w/ 7 levels "APR","AUG","JUL",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ day : int 10 11 12 13 14 15 23 24 25 27 ...
## $ attend : int 56000 29729 28328 31601 46549 38359 26376 44014 26345 44807 ...
## $ day_of_week: Factor w/ 7 levels "Friday","Monday",..: 6 7 5 1 3 4 2 6 7 1 ...
## $ opponent : Factor w/ 17 levels "Angels","Astros",..: 13 13 13 11 11 11 3 3 3 10 ...
## $ temp : int 67 58 57 54 57 65 60 63 64 66 ...
## $ skies : Factor w/ 2 levels "Clear ","Cloudy": 1 2 2 2 2 1 2 2 2 1 ...
## $ day_night : Factor w/ 2 levels "Day","Night": 1 2 2 2 2 1 2 2 2 2 ...
## $ cap : Factor w/ 2 levels "NO","YES": 1 1 1 1 1 1 1 1 1 1 ...
## $ shirt : Factor w/ 2 levels "NO","YES": 1 1 1 1 1 1 1 1 1 1 ...
## $ fireworks : Factor w/ 2 levels "NO","YES": 1 1 1 2 1 1 1 1 1 2 ...
## $ bobblehead : Factor w/ 2 levels "NO","YES": 1 1 1 1 1 1 1 1 1 1 ...# Evaluate the factor levels for day_of_week
# levels(DodgersData$day_of_week)
# Reorder the factor levels for day_of_week
DodgersData$day_of_week <- factor(DodgersData$day_of_week, levels = c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"))
# Evaluate the factor levels for month
# levels(DodgersData$month)
# Reorder the factor levels for month
DodgersData$month <- factor(DodgersData$month, levels = c("APR", "MAY", "JUN", "JUL", "AUG", "SEP", "OCT"))
# First 10 rows of the data frame
head(DodgersData, 10)## month day attend day_of_week opponent temp skies day_night cap shirt
## 1 APR 10 56000 Tuesday Pirates 67 Clear Day NO NO
## 2 APR 11 29729 Wednesday Pirates 58 Cloudy Night NO NO
## 3 APR 12 28328 Thursday Pirates 57 Cloudy Night NO NO
## 4 APR 13 31601 Friday Padres 54 Cloudy Night NO NO
## 5 APR 14 46549 Saturday Padres 57 Cloudy Night NO NO
## 6 APR 15 38359 Sunday Padres 65 Clear Day NO NO
## 7 APR 23 26376 Monday Braves 60 Cloudy Night NO NO
## 8 APR 24 44014 Tuesday Braves 63 Cloudy Night NO NO
## 9 APR 25 26345 Wednesday Braves 64 Cloudy Night NO NO
## 10 APR 27 44807 Friday Nationals 66 Clear Night NO NO
## fireworks bobblehead
## 1 NO NO
## 2 NO NO
## 3 NO NO
## 4 YES NO
## 5 NO NO
## 6 NO NO
## 7 NO NO
## 8 NO NO
## 9 NO NO
## 10 YES NOExploratory analysis (explained)
The results show that in 2012 there were a few promotions
Cap
Shirt
Fireworks
BobbleheadWe have data from April to October for games played in the Day or Night under Clear or Cloudy Skys.
Dodger Stadium has a capacity of about 56,000. Looking at the entire (sample) data shows that the stadium filled up only twice in 2012. There were only two cap promotions, three shirt promotions - not enough data for any inferences. Fireworks and Bobblehead promotions have happened a few times.
Further more there were eleven bobble head promotions and most of then (six) being on Tuesday nights.
Attendance by Day Of Week/month
## Box plot to explore attendance by day of week
plot(DodgersData$day_of_week, DodgersData$attend / 1000, main = "Dodgers Attendence By Day Of Week", xlab = "Day of Week", ylab = "Attendance (thousands)", col = "violet", las = 1)
## Box plot to explore attendance by Month
plot(DodgersData$month, DodgersData$attend / 1000, main = "Dodgers Attendence By Month", xlab = "Month",
ylab = "Attendance (thousands)", col = "light blue", las = 1)
Evaluate Attendance by Weather
#Evaluate attendance by weather
ggplot(DodgersData, aes(x=temp, y=attend/1000, color=fireworks)) +
geom_point() +
facet_wrap(day_night~skies) +
ggtitle("Dodgers Attendance By Temperature By Time of Game and Skies") +
theme(plot.title = element_text(lineheight=3, face="bold", color="black", size=10)) +
xlab("Temperature (Degree Farenheit)") +
ylab("Attendance (Thousands)")
Strip Plot of Attendance by opponent or visiting team
#Strip Plot of Attendance by opponent or visiting team
ggplot(DodgersData, aes(x=attend/1000, y=opponent, color=day_night)) +
geom_point() +
ggtitle("Dodgers Attendance By Opponent") +
theme(plot.title = element_text(lineheight=3, face="bold", color="black", size=10)) +
xlab("Attendance (Thousands)") +
ylab("Opponent (Visiting Team)")
Design Predictive Model
To advise the management if promotions impact attendance we will need to identify if there is a positive effect, and if there is a positive effect how much of an effect it is.
To provide this advice, I built a Linear Model for predicting attendance using Month, Day Of Week and the indicator variable Bobblehead promotion. I split the data into Training and Test to create the model
# Create a model with the bobblehead variable entered last
my.model <- {attend ~ month + day_of_week + bobblehead}
# Prepare a Training and Test dataset
# Reseed for repeatability
set.seed(1234)
training_test <- c(rep(1, trunc((2/3)*nrow(DodgersData))), rep(2, trunc((1/3)*nrow(DodgersData))))
# sample(training_test)
# Create a variable in DodgersData data frame to identify Test and Training row
DodgersData$Training_Test <- sample(training_test)
DodgersData$Training_Test <- factor(DodgersData$Training_Test, levels = c(1, 2), labels = c("TRAIN", "TEST"))
DodgersData.Train <- subset(DodgersData, Training_Test == "TRAIN")
DodgersData.Test <- subset(DodgersData, Training_Test == "TEST")
#head(DodgersData.Train)
#head(DodgersData.Test)
# Fit model to training set
train.model.fit <- lm(my.model, data = DodgersData.Train)
# Predict from Training Set
DodgersData.Train$Predict_Attend <- predict(train.model.fit)
# Evaluate The Fitted Model on the Test Set
DodgersData.Test$Predict_Attend <- predict(train.model.fit, newdata = DodgersData.Test)
#round(cor(DodgersData.Test$attend, DodgersData.Test$Predict_Attend)^2, digits=3)
# compute the proportion of response variance accounted for when predicting Test Data
cat("\n","Proportion of Test Set Variance Accounted for: ", round(cor(DodgersData.Test$attend, DodgersData.Test$Predict_Attend)^2, digits=3), "\n", sep="")##
## Proportion of Test Set Variance Accounted for: 0.453Use scatter plots to evaluate fit of the model
DodgersData.Training_Test <- rbind(DodgersData.Train, DodgersData.Test)
ggplot(DodgersData.Training_Test, aes(x=attend/1000, y=Predict_Attend/1000, color=bobblehead)) +
geom_point() +
geom_line(data = data.frame(x = c(25,60), y = c(25,60)), aes(x = x, y = y), colour = "red") +
facet_wrap(~Training_Test) +
#geom_smooth(method = "lm", se=FALSE) +
ggtitle("Regression Model Performance : Bobblehead and Attendance") +
theme(plot.title = element_text(lineheight=3, face="bold", color="black", size=10)) +
xlab("Actual Attendance (Thousands)") +
ylab("Predicted Attendance (Thousands)")
Run the model on the entire Dodgers Data Set
# use the full data set to obtain an estimate of the increase in
# attendance due to bobbleheads, controlling for other factors
my.model.fit <- lm(my.model, data = DodgersData) # use all available data
print(summary(my.model.fit))##
## Call:
## lm(formula = my.model, data = DodgersData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10786.5 -3628.1 -516.1 2230.2 14351.0
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33909.16 2521.81 13.446 < 2e-16 ***
## monthMAY -2385.62 2291.22 -1.041 0.30152
## monthJUN 7163.23 2732.72 2.621 0.01083 *
## monthJUL 2849.83 2578.60 1.105 0.27303
## monthAUG 2377.92 2402.91 0.990 0.32593
## monthSEP 29.03 2521.25 0.012 0.99085
## monthOCT -662.67 4046.45 -0.164 0.87041
## day_of_weekTuesday 7911.49 2702.21 2.928 0.00466 **
## day_of_weekWednesday 2460.02 2514.03 0.979 0.33134
## day_of_weekThursday 775.36 3486.15 0.222 0.82467
## day_of_weekFriday 4883.82 2504.65 1.950 0.05537 .
## day_of_weekSaturday 6372.06 2552.08 2.497 0.01500 *
## day_of_weekSunday 6724.00 2506.72 2.682 0.00920 **
## bobbleheadYES 10714.90 2419.52 4.429 3.59e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6120 on 67 degrees of freedom
## Multiple R-squared: 0.5444, Adjusted R-squared: 0.456
## F-statistic: 6.158 on 13 and 67 DF, p-value: 2.083e-07Reference
This case study is originally from Modeling Techniques in Predictive Analysis by Thomas W. Miller. Thank you, Dr. Miller!
This book a must-read for digital marketers!!! Enjoy and have fun!